Conjectures REF (ii) and (iv) were settled, respectively,
in [1]} and [2]}.
Furthermore in [1]} it was shown that
\(\mathcal {I}_{2p}=\lbrace 1,2\rbrace \)  for every odd prime \(p\)  and a complete
characterization of groups of degree \(2p\)  with
intersection density 2 was also given there.
In Proposition REF 
we show that Conjecture REF (iii)
is true for transitive groups
of degree \(pq\) , \(p>q\)  odd primes, which contain a transitive
subgroup with blocks of size \(p\) .
Moreover, as a main result of this paper we give a construction
of transitive groups of degree \(pq\)  with blocks of size \(q\)  and
intersection density \(q\)  (see Theorem REF  below).
Consequently Conjecture REF (iii) is not true.
